Can you get a drivers license in Texas if you have a suspended one in another state?

No if you are suspended in one state every other state recognizes the suspension and will not issue you one.

The above answer is wrong. Colorado has an administrative regulation

(1 CCR 204-16 Interstate Driver's License Compact) that allows the DMV to issue a driver's license despite holds, cancellations, revocations and even lifetime bans. Colorado is in the compact (Massachusetts is the fifth state that doesn't participate BTW) but will issue a license after a hearing while recognizing the other state's revocation. James Forslund is an attorney who has been providing this service for about 10 years.

All states are members except for Georgia, Michigan, Wisconsin, Tennessee (dropped out in 1997). Nevada repealed the authorizing legislation in 2007[1], though it still generally conforms to the agreement through regulations.